Yeah, Vash would gain access to tons of places by staying with the enterprise. I guess starfleet wouldn't like that very much though.
Or Starfleet might look at it from the point of view that they always know where Vash is and what she is doing. The situation giving them the ability to direct her talents to a more productive use.
Or Starfleet might not care. Kasidy Yates married Sisko after doing jail time for smuggling.
Most likely her past antics (which are no different then other archeologists we've seen in canon) would be taken lightly or just ignored and future antics would be toned down. That whole speed of plot thing.